Modifying the Black-Scholes-Merton model to calculate the cost of employee stock options

Purpose - – More than 80 percent of S&P 500 firms that issue ESOs use the Black-Scholes-Merton (BSM) model and substitute the estimated average term for the contractual expiration to calculate ESO expense. This simplification systematically overprices ESOs, which worsens as the stock's volatility increases. The purpose of this paper is to present a modification of the BSM model to explicitly incorporate the rates of forfeiture pre- and post-vesting and the rate of early exercise. Design/methodology/approach - – The paper demonstrates the model's usefulness by employing historical exercise and forfeiture data for 127 separate ESO grants and 1.31 billion ESOs to calculate the exercise and forfeiture parameters and value ESOs for nine firms. Findings - – The modified BSM model is just as accurate but easier to use than the more computationally intensive utility maximization and trinomial lattice models, and it avoids the ASC 718 BSM model's overpricing bias. Originality/value - – If firms prefer the BSM model over more mathematically elegant alternatives, they should at least use a BSM model that is free of overpricing bias.